Measurement of Young's Modulus. 407 



same level as the knife-edges. Then the equation of motion 

 of the bifilar oscillation when the wires are distant 2c apart is 



M* 1 *0=-(M0j+2t)0, 



and the frequency n x is given by 



Similarly the frequency n{ when the wires are distant 2d 

 apart is given by 



therefore 



47r 2 Z; 1 2 (n 1 2 -n/ 2 ) =|(c 2 -^ 2 ). . . . (1). 



Again the equation of motion for the pitching oscillation 

 when the wires are distant 2c apart is 



and the frequency n 2 is given by 



Likewise the frequency of pitching nj when the wires are 

 distant 2d apart is given by 



Therefore 



47r^(» 2 2 -n 2 ' 2 ) = |](o 2 -^). ... (2) 

 Consequently 



*-»^ < 3 > 



a result requiring no measurement except the periods and 

 the weight of the needle. 



Secondly, if the centre of gravity of the needle is at a 

 distance x below the level of the knife-edges the equation of 

 motion for pitching with the wires 2e apart is 



